We will solve this problem by substituting mx - 10 for y in the equation of the parabola and then write down the condition for the resulting quadratic equation to have equal roots (the line and the parabola have 1 point in common)

y = mx - 10 meets y = 3x² + 7x + 2 in one point

mx - 10 = 3x² + 7x + 2

3x² + (7-m)x + 12 = 0

The roots are equal if

(7-m)² - 4*3*12 = 0

m² - 14m + 49 - 144 = 0

m² - 14m - 95 = 0

(m - 19)(m + 5) = 0

m = 19 or -5

the lines y = 19x - 10 and y = - 5x - 10 are tangents of the parabola y= 3x^2 + 7x + 2.